#9138: Categories for all rings
---------------------------------+------------------------------------------
Reporter: jbandlow | Owner: nthiery
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.7.1
Component: categories | Keywords: introspection, categories
for rings
Work_issues: Steenrod algebras | Upstream: N/A
Reviewer: | Author: Simon King
Merged: | Dependencies: sage-4.7, #11268, #11139,
#9976, #9944, #11269
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Comment(by SimonKing):
Replying to [comment:69 SimonKing]:
> I think the easiest solution (and probably the best solution as well
would be to replace that test by a polynomial ring over a different non-
commutative algebra, perhaps a matrix algebra.
Helàs.
Matrix spaces have their custom `__getitem__` as well. But it would be
possible to construct the polynomial ring by using the polynomial ring
constructor:
{{{
sage: PolynomialRing(MatrixSpace(QQ,2),'x').category()
Category of algebras over Full MatrixSpace of 2 by 2 dense matrices over
Rational Field
sage: PolynomialRing(SteenrodAlgebra(2),'x').category()
Category of algebras over mod 2 Steenrod algebra, milnor basis
}}}
The other problem is in sage/algebras/steenrod/steenrod_algebra.py.: With
the patch from here,
{{{
sage: A1 = SteenrodAlgebra(profile=[2,1])
sage: A1(3) # map integer into A1
}}}
returns 3 and not 1!
That behaviour boils down to
{{{
sage: A1._from_dict({():3})
3
}}}
Here, one should have
{{{
sage: A1._from_dict({():3},coerce=True)
1
}}}
I don't know, though, how my patch has changed the question whether there
is a conversion or not: The word `coerce` occurs precisely twice in my
first patch, but that is certainly unrelated with "coerce=True" versus
"coerce=False". Strange.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9138#comment:70>
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